In this paper we pursue the refined global Gross-Prasad conjecture for Bessel periods formulated by Yifeng Liu in the case of special Bessel periods for SO(2n+1)×SO(2). Recall that a Bessel period for SO(2n+1)×SO(2) is called special when the representation of SO(2) is trivial. Let π be an irreducible cuspidal tempered automorphic representation of a special orthogonal group of an odd dimensional quadratic space over a totally real number field F whose local component πv at any archimedean place v of F is a discrete series representation. Let E be a quadratic extension of F and suppose that the special Bessel period corresponding to E does not vanish identically on π. Then we prove the Ichino-Ikeda type explicit formula conjectured by Liu for the central value L(1/2,π)L(1/2,π×χE), where χE denotes the quadratic character corresponding to E. Our result yields a proof of B\"ocherer's conjecture on holomorphic Siegel cusp forms of degree two which are Hecke eigenforms.